United said owners will have to confirm that their animal is trained to behave in public, and they will need a vaccination form signed by a veterinarian. The vet will have to vouch that the animal isn't a health or safety threat to other people.

"United has seen a 75 percent year-over-year increase in customers bringing emotional support animals onboard and has experienced a significant increase in onboard incidents involving these animals," the airline said in a statement. "We understand that other carriers have seen similar trends. The Department of Transportation's rules regarding emotional support animals are not working as they were intended, and we need to change our approach in order to ensure a safe and pleasant travel experience for all of our customers."

The airline bounced a passenger on Sunday who showed up at the airport with a peacock for emotional support. New York City-based photographer and performance artist Ventiko said she bought a ticket for her peacock, Dexter, so he would have his own seat on Sunday's flight from New Jersey's Newark Liberty International Airport to Los Angeles.

United already bans exotic animals and non-household birds. Still, the fact that a passenger tried to bring a peacock on board "helped illustrate why we needed to revise our policy," United spokesman Charles Hobart said.

Guide dogs have been occasional flyers for years, but recently there has been a surge of emotional-support animals. Federal regulations allow them -- if they're not too big or exotic -- but airlines can ask for a doctor's note verifying that the passenger needs the animal.

Airlines are convinced that scofflaws abuse the rules. Passengers often have to pay $125 or more each way to bring a small pet on board, but comfort animals fly free.

The crackdown by Delta raised objections from service-dog owners. Jenine Stanley of the Guide Dog Foundation for the Blind is upset that Delta will require service-dog owners to file a health form at least 48 hours before a flight. That could make emergency trips impossible.

"I don't think I've ever filled out a form for assistance. Now my animal is going to have to be verified every time," she said.

United said it will not require forms for trained service animals. It's unclear, however, what would stop someone from claiming their comfort animal is a trained service animal.

The Association of Flight Attendants-CWA (AFA) -- a union -- has praised United's announcement, saying the airline has taken "a very thoughtful, responsible approach to this issue," CBS News' Kris Van Cleave reports.

"The airline's increased requirements for emotional support animals will reduce fraud and protect the legitimate need of animal assistance for passengers with disabilities and veterans," Sara Nelson, international president of AFA, said Thursday in a statement. "This is about maintaining safety, health and security for passengers and crew, while ensuring accessibility for those who need it."